Problem: Solve for $x$ and $y$ using elimination. ${-2x+y = -5}$ ${-3x-y = -25}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-5x = -30$ $\dfrac{-5x}{{-5}} = \dfrac{-30}{{-5}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-2x+y = -5}\thinspace$ to find $y$ ${-2}{(6)}{ + y = -5}$ $-12+y = -5$ $-12{+12} + y = -5{+12}$ ${y = 7}$ You can also plug ${x = 6}$ into $\thinspace {-3x-y = -25}\thinspace$ and get the same answer for $y$ : ${-3}{(6)}{ - y = -25}$ ${y = 7}$